# Relative Motion, a confusion

• Lillyotv
In summary: It's actually more general than that.The analogous argument holds for the Galilean transformations as well.
Lillyotv
What two speed measurements do two observers in relative motion always agree on?

In my opinion, one will be relative velocity...but can't figure out the other..?
Any ideas?

Also, photons of light have zero mass. How is it possible that they momentum?

Cuz Momentum=mv...so if m is zero then how come they have momentum?...I thought abt this and researched...I think the reason is that photons don't have particle properties...kindly elaborate why exactly?

The other speed that they will agree on -- of course -- is the speed of light.

Photons have no "rest mass". If they did, they would require infinite energy to move at the speed of light. The equation 'momentum=mv' is from classical mechanics which is no longer regarded as exactly correct. Both relativity and quantum mechanics forced some modifications on to it. Look up 'relativistic momentum' for more detail.

speed of light is the only absolute I can think of. I can see where you might think relative motion but what if the "motion" were "quick" enough to cause time dilation. Well then distance / time would become a quagmire. So my vote is for the speed of light only!

It has nothing to do with time dilation. Lillyotv is correct. The relative speeds will be the same: The speed of B relative to A is the same as the speed of A relative to B.

Doc Al said:
It has nothing to do with time dilation. Lillyotv is correct. The relative speeds will be the same: The speed of B relative to A is the same as the speed of A relative to B.
So, it will be 2 speeds...just relative to each other..now that makes sense...thanks!

Doc Al said:
It has nothing to do with time dilation. Lillyotv is correct. The relative speeds will be the same: The speed of B relative to A is the same as the speed of A relative to B.
I read a book where this was assumed without any proof. Is it possible to prove this?

Lojzek said:
I read a book where this was assumed without any proof. Is it possible to prove this?
One way is to use the relativistic addition of velocities:
$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

In this case:
$$V_{a/a} = \frac{V_{a/b} + V_{b/a}}{1 + (V_{a/b} V_{b/a})/c^2}$$

Since:
$$V_{a/a} = 0$$

Therefore:
$$V_{a/b} = - V_{b/a}$$

Make sense?

Lojzek said:
I read a book where this was assumed without any proof. Is it possible to prove this?

If you think geometrically, it may be obvious.
All particle 4-velocities are, in spacetime, unit-vectors whose tips lie on the unit future-hyperboloid (analogous to a sphere in Euclidean space).

Relative-speed is simply [the speed of light times] the hyperbolic-tangent of the unsigned "angle" intercepted by the two 4-velocities being considered. (This "angle" is essentially an arc-length on the unit-hyperboloid.)

This is the geometrical picture underlying Doc Al's post.

The problem is that last two answers are based on validity of Lorentz transformation. That book I mentioned included derivation of Lorentz transformation from the assumption that two observers see each other traveling with equal, but opposite speeds: v(A,B)=-v(B,A). The assumption was needed to obtain equation L(v)*L(-v)=Identity.

So we must either prove the statement in question without using Lorentz transformation
or derive Lorentz transformation without this assumption!

Lojzek said:
The problem is that last two answers are based on validity of Lorentz transformation. That book I mentioned included derivation of Lorentz transformation from the assumption that two observers see each other traveling with equal, but opposite speeds: v(A,B)=-v(B,A). The assumption was needed to obtain equation L(v)*L(-v)=Identity.

So we must either prove the statement in question without using Lorentz transformation
or derive Lorentz transformation without this assumption!

It's actually more general than that.
The analogous argument holds for the Galilean transformations as well.

## 1. What is relative motion?

Relative motion is the movement of an object in relation to another object or point of reference. It is the perception of motion from a specific observer's point of view.

## 2. How does relative motion differ from absolute motion?

Absolute motion is the actual, measurable movement of an object in space. Relative motion takes into account the perspective of the observer and how they perceive the motion of the object.

## 3. What factors can affect relative motion?

The relative motion of an object can be affected by the speed and direction of the object, as well as the distance and perspective of the observer.

## 4. Can relative motion be used to calculate the speed of an object?

No, relative motion does not provide an accurate measurement of an object's speed. It only describes the perceived movement of an object in relation to another object or point of reference.

## 5. How is relative motion used in scientific research?

Relative motion is often used in scientific research to understand and explain the movement and interactions of objects. It can also be used to determine the position and direction of an object in relation to other objects or points of reference.

• Special and General Relativity
Replies
19
Views
2K
• Special and General Relativity
Replies
26
Views
607
• Special and General Relativity
Replies
84
Views
4K
• Special and General Relativity
Replies
21
Views
1K
• Special and General Relativity
Replies
32
Views
951
• Special and General Relativity
Replies
15
Views
916
• Special and General Relativity
Replies
45
Views
3K
• Special and General Relativity
Replies
25
Views
559
• Special and General Relativity
Replies
1
Views
1K
• Special and General Relativity
Replies
28
Views
2K